Cation exchange membranes used in electrolysis are required to have small electrical resistance, high resistance to oxidation, acids, alkalies, and great compression strength. Cation exchange membranes known to have these properties are perfluorocarbon membranes having sulfonyl-containing side chains, and most of them are produced as copolymer of a perfluorovinyl compound and a sulfonyl-containing monomer. For details of the method for producing them, see U.S. Pat. Nos. 3,784,399, 3,770,567 and 3,909,378. Although these membranes have good properties, their price is very high since the preparation of the perfluorocarbon monomer used as one of the starting materials involves a number of steps and costs much. A process has been proposed to produce an ion exchange membrane by grafting a sulfonyl-containing monomer onto a fluorovinyl polymer (see Japanese Patent Public Disclosure No. 32289/75), but since the perfluorocarbon polymer is generally less inert to radiation and is less susceptible to grafting of monomers and because the monomer to be grafted does not penetrate deep into the polymer, it has been technically difficult to have the monomer grafted uniformly in the interior of a perfluorocarbon polymer substrate. It is therefore difficult in the state of the art to produce a uniform cation exchange membrane with small electrical resistance by the process described in Japanese Patent Public Disclosure No. 32289/75.